Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-2450.1-j
Conductor 2450.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{2}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).

Elliptic curves in class 2450.1-j over \(\Q(\sqrt{2}) \)

Isogeny class 2450.1-j contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
2450.1-j1 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -156 a + 200\) , \( 210 a - 373\bigr] \)
2450.1-j2 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 3 a + 2\) , \( -18 a - 25\bigr] \)
2450.1-j3 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -47 a - 98\) , \( -258 a - 305\bigr] \)
2450.1-j4 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 469 a - 1050\) , \( 460 a - 4123\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph